Mange can be a frustrating condition. I would bathe with DEFENDEX shampoo once or twice weekly for 4-6 weeks or a couple of weeks past having a negative skin scraping. The shampoo is very concentrated so just use a small amount. This is a less toxic approach than the conventional dips and it has worked better in some cases. Be sure to wash bedding and grooming tools.
I would also use the homeopathic DERMA-IONX both internally and externally to heal and soothe the skin as well as rebuilding the immune system. Giving probiotics, vitamin C, and Omega 3,6,9 will all help in that goal. DERMA-IONX also helps the body to better utilize the supplements for faster results. I would start with a 1/2 dose of DERMA-IONX twice a day. It is easiest to add it to the food. I would feed a grain free dog food. I would offer filtered drinking water to avoid chlorine or fluoride.
To work on the fatty tumor you could try acupuncture. Try to find a veterinarian that has been trained in TCVM (Traditional Chinese Veterinary Medicine). In TCVM a fatty tumor is a sign of stagnation and the acupuncturist tries to dissipate stagnation.
Please let us know how you progress or if you have any other questions.